# Pre-Order Montessori Geometry for the Adolescent

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This is the pre-order price for Michael Waski’s new book, Montessori Geometry for the Adolescent. Get the pre-order price and have the book by mid-October!

Table of Contents

I. Introduction

II. Chapter of Logic

A. Guess My Number Game

B. Other Games

1. Color Square Game

2. Clueless Crosswords

3. Other Games

III. Chapter of Constructions

A. Euclid’s Definitions

B. The MU-Puzzle

C. Euclid’s Axioms or Postulates

D. The Parallel Postulate and Spherical Geometry

E. Common Notions

F. The Six Basic Constructions

1. Constructing an Equilateral Triangle

2. Constructing a Perpendicular Bisector

3. Constructing a Perpendicular through a Point on the Line

4. Constructing a Perpendicular through a Point not on the Line

5. Constructing an Angle Bisector

6. Copying an Angle

G. Construction Extensions and Activities

1. Geometric Constructions Itinerary

a) Construction Instructions

2. Sample Projects

3. Constructions Applications Project

4. Construction Artwork

5. Euclid’s Elements Project

6. Nepal Flag Construction

7. Regular Polygons

IV. Chapter of Angles

A. Angle Definition and Measure

B. Types of Angles

C. Measuring Angles

D. Degrees, Minutes, and Seconds

E. Naming Angles

F. Angle Relations

1. Adjacent Angles

2. Complementary and Supplementary Angles

a) Complementary and Supplementary Angles

b) Polygon Exploration

3. Vertical Angles

G. Angles with Transversals

1. Angles with Transversals

2. Transversals with Parallel Lines

3. Proofs

H. Interior Angles of a Triangle

I. Exterior Angles of a Triangle Theorem

J. Isosceles Triangle Theorem

K. Puzzles with Angle Relations

L. Templates for Proofs

M. Further Work with Angles

V. Chapter of Congruency

A. Congruency Definition

B. Determining if Figures are Congruent

C. Triangle Congruency Theorems

1. Side-Side-Side (SSS)

2. Triangle Inequality Theorem

3. Angle-Angle-Angle (AAA)

4. Side-Angle-Side (SAS)

5. Angle-Side-Angle (ASA)

6. Angle-Angle-Side (AAS)

7. Side-Side-Angle (SSA)

D. Proofs Using Congruency Theorems

VI. Chapter of Polygons

A. Triangles

1. Naming Triangles

2. Parts of Triangles

3. Centers of Triangles

B. Quadrilaterals

1. Naming and Classification of Quadrilaterals

2. Parts of Quadrilaterals

C. Other Polygons

1. Naming Other Polygons

2. Types of Polygons

3. Parts of Polygons

4. Interior Angles of Polygons

5. Exterior Angles of Polygons

VII. Chapter of Linear Measurement

A. Perimeter

B. The Pythagorean Theorem

1. Discovering the Pythagorean Theorem

2. Formal Presentation of the Pythagorean Theorem

3. Applying the Pythagorean Theorem

4. Formal Proofs of the Pythagorean Theorem

C. Pythagorean Theorem in Three Dimensions

D. Special Right Triangles

E. Further Pythagorean Extensions

VIII. Chapter of Area

A. Areas on Dot Paper

B. Estimating Area

C. The Yellow Material

D. Area of Rectangles and Squares

E. Area of Parallelograms

F. Area of Triangles

G. Area of Trapezoids

H. Area of Rhombi and Kites

I. Area of Regular Polygons

J. Area of Circles

K. Compound Areas and Interstices

L. Pick’s Theorem

M. Area of Triangles without Base and Height

1. Law of Sines Formula

2. Heron’s Formula

3. Area Given Coordinates

IX. Chapter of Circles

A. Parts of a Circle

B. Relationships Between Circles

C. Discovery of Pi

D. Circumference

1. Circumference of a Circle

2. Arc Length

E. Area

1. Areas Involving Circles

2. Area of a Sector

3. Area of Lunes

F. Angles of a Circle

1. Central Angles and Arc Measure

2. Central Angles and the Circumference of the Earth

3. Inscribed Angles

G. Lines through a Circle

1. Tangents to Circles

2. Constructing the Center of a Circle

3. Angles Formed by Secants and Tangents

4. Proportions with Chords, Secants, and Tangents

5. Ptolemy’s Theorem

X. Chapter of Solid Geometry

A. Isometric Drawings

B. Hidden Cubes Activity

C. Building Boxes Activity

D. Names and Parts of Prisms and Pyramids

E. The Platonic Solids

F. Building Solids

G. Euler’s Formula

H. Surface Area

I. Volume

1. Volume, and Volume of Right Prisms

2. Volume of Oblique Prisms

3. Volume of Pyramids

4. Volume of a Sphere

5. Surface Area of a Sphere

XI. Chapter of Similarity

A. Similarity

B. Finding Unknown Sides of Similar Shapes

C. Similar Triangles with Parallel Lines and Right Triangles

D. On Being the Right Size

E. Ratios of Area and Volume

F. Similarity Projects

G. Introduction to Similarity with Extensions to Trigonometry